Back in Shanghai again for the fourth institute! Moving past the vast, unmanageable resources such as Engage & adapting to our students and classes. General and random notes and thoughts.
Geo-metry: measurement of the Earth
A balanced brain –> numerical, verbal, spatial
What is Geometry
- study of shapes
- relationships between objects
- connection of mathematics to the physical world
- dimensions (point, line, plane,
- space
- logic / reasoning
- making / defending conjectures
Connection of geometry to number & algebra
- bar models – multiplication area models
- number lines – Cartesian plane
- distribute property
- tables to graphs
- composing & decomposing (shapes like numbers & expressions)
Data – clumps, bumps and holes
Van Hiele Levels
- Identify – name
- Draw – create
- Describe – characteristics
- Analyze – properties, examples & counterexamples
- Classify / categorize
Language: informal to formal + Picture
Measurement
- benchmarks or referents are essential
- Number is discrete, measurement is continuous
- Estimation is essential
- an approximation with tools (i.e. nearest kilogram)
- measurement conversion similar to common denominator (must have same to compare / work with)
Resource Reminder – spend 5 minutes on LearnZillion to see how they unpack the standard.
Day 2
Justification – Give problems more ambiguity. Justification involves explaining why certain mathematical decisions were made.
PreK-2 Progressions of Measurement
- Describe and compare measurable attributes
- Measure lengths indirectly and by iterating length units
- Order first (G1) then measure (G2)
- G1: express length as whole number of length units spanning with no gaps or overlaps. End to end
- G2: measure with different units, estimate lengths, how much longer is one than another
- Relate addition and subtraction to length
- PreK – directly compare, “more of / less of”
- G2 – using number lines
- Tell & write time (G1-G2) Note: G2 begins with money as well (not quite sure what that has to do with time)
- Classify objects and count the number of objects in each
- PreK – sort
- K – classify & count
- Represent and interpret data
- PreK: Compare categories (greater than / less than…)
- G1 – Organize, represent and interpret data with up to 3 categories
- G2 – generate measurement data. Make line plots of whole number units
Geometry
- Identify & describe shapes
- PreK – match like shapes, group by attributes, correctly name
- K – Describe objects using their name s and relative positions, identify shapes as 2-dimensional (flat) or 3-dimensional (solid)
- Analyze, compare, create & compose shapes
- PreK – describe 3d objects
- K – analyze & compare 2D / 3D shapes, model shapes by building, compose simple shapes to form larger shapes
- G1-distinguish between defining attributes (e.g. triangles are closed & 3D) versus non-defining attributes (color, orientation, size…)
- build shapes
- draw shapes
- compose 2D shapes or 3D shapes to make composite shapes
- Partition circles & rectangles (halves, fourths, quarters)
- G2-Recognize & draw shapes with specified attributes
- partition rectangles into rows & columns. Count to find total number
- partition circles & rectangles into shares. Describe, and recognize part:whole
Notes looking from 3 to 7
- Rectangles are hammered in the lower grades. 2D, 3D. Area. Volume.
- Circles pop up in 7th but have not been discussed since 2nd grade. Wow! Students might not know these key vocabulary terms.
- Angles have not been discussed since 4th grade
- Triangles are worked on in 6th
- Scale drawings are new – build upon ratios
Big Middle School Ideas
- Circles (pi)
- Pizza is 78% of the pizza box
- Pythagorean Theorem (G8)
- Using formulas (generalization of relationships)
- Why do they work?
- Surface Area
- Transformations – Scale
- Congruence & Similarities (G8)
- Lines & Angles
- Begin becoming more precise of justification
Finding the Process 